CUET UG 2025 — General Test Geometry

2025mcqmedium

If the area of an equilateral triangle is $36\sqrt{3}$ cm², then the length of the side is:

Official previous-year question

Held on 27 May 2025 · Verified 13 Jul 2026.

Options

A
12 cm
B
9 cm
C
6 cm
D
3 cm

Did you get this right?

Solution

The area of an equilateral triangle with side length $a$ is given by:

Area $= \dfrac{\sqrt{3}}{4} \times a^2$

Given that the area is $36\sqrt{3}$ cm²:

$36\sqrt{3} = \dfrac{\sqrt{3}}{4} \times a^2$

Multiplying both sides by $4$ :

$144\sqrt{3} = \sqrt{3} \times a^2$

Dividing both sides by $\sqrt{3}$ :

$\dfrac{144\sqrt{3}}{\sqrt{3}} = a^2$

$144 = a^2$

Taking the square root of both sides:

$a = \sqrt{144}$

$a = 12$

Therefore, the length of the side is $12$ cm.

Your note

CUET UG Geometry in other years

Geometry 2024 Geometry 2023 Geometry 2022

Keep practicing Geometry

Work through every CUET UG Geometry PYQ, year by year.

Browse all General Test topics

CUET UG 2025 — General Test Geometry

2025mcqmedium

If the area of an equilateral triangle is $36\sqrt{3}$ cm², then the length of the side is:

Official previous-year question

Held on 27 May 2025 · Verified 13 Jul 2026.

Options

A
12 cm
B
9 cm
C
6 cm
D
3 cm

Did you get this right?

Solution

The area of an equilateral triangle with side length $a$ is given by:

Area $= \dfrac{\sqrt{3}}{4} \times a^2$

Given that the area is $36\sqrt{3}$ cm²:

$36\sqrt{3} = \dfrac{\sqrt{3}}{4} \times a^2$

Multiplying both sides by $4$ :

$144\sqrt{3} = \sqrt{3} \times a^2$

Dividing both sides by $\sqrt{3}$ :

$\dfrac{144\sqrt{3}}{\sqrt{3}} = a^2$

$144 = a^2$

Taking the square root of both sides:

$a = \sqrt{144}$

$a = 12$

Therefore, the length of the side is $12$ cm.

Your note

CUET UG Geometry in other years

Geometry 2024 Geometry 2023 Geometry 2022

Keep practicing Geometry

Work through every CUET UG Geometry PYQ, year by year.

Browse all General Test topics

CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry

CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry